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infinite set

   Also found in: Wikipedia 0.01 sec.
infinite set [′in·fə·nət ′set]
(mathematics)
A set with more elements than any fixed integer; such a set can be put into a one to one correspondence with a proper subset of itself.
(mathematics)infinite set - A set with an infinite number of elements. There are several possible definitions, e.g.

(i) ("Dedekind infinite") A set X is infinite if there exists a bijection (one-to-one mapping) between X and some proper subset of X.

(ii) A set X is infinite if there exists an injection from N (the set of natural numbers) to X.

In the presence of the Axiom of Choice all such definitions are equivalent.
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The sources of ambiguity are: infinite set, large or small number (depending on context), self-reference, e.
SOME IMPORTANT INFORMATION ABOUT THE NEW REAL NUMBER SYSTEM by E. E. Escultura / Biological sciences community
This is because Pirahã language apparently lacks what is known as 'recursion', the process by which relative clauses are embedded in sentences to produce an infinite set of possibilities.
Lost for words in the Amazon by guardian.co.uk / guardian.co.uk
McLennan offers the example of an auction in which each bidder can bid any amount--mathematically, an infinite set of numbers.
Nash's math gets more beautiful: even with infinite choices, games ... by Barry, Patrick / Science News
 
 
 
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